Assessment of different 1d numerical schemes for steady flows over a geometrical discontinuity.

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Fabian Franzini, Javier Murillo, Sandra Soares-Frazão

Thursday 2 july 2015

12:00 - 12:15h at Oceania (level 0)

Themes: (T) Water engineering, (ST) Computational methods

Parallel session: 11E. Engineering - Computational

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In order to model fast transient flows in rivers following a dam break, the shallow water equations are solved by means of several finite volume schemes. One of the most well-known is the Roe’s scheme. However, this method was initially created for cases without source terms. Moreover, the flood waves’ behavior is often dictated by strong source terms due to the bed friction or irregular topography. Thus, an adaptation of the method is needed. The scheme used in this work is a 1D Augmented Roe’s solver with energy balance developed by Murillo and Garcia-Navarro (2014). It modifies the classical 1D Roe’s scheme in two ways. First, the source terms are represented by an increase of the number of intermediate states. Then, the topographical source terms are integrated to enforce energy conservation, outside of a shock. The results of this scheme are accurate for many test cases but one, the simulation of a transcritical flow with a shock over a geometrical discontinuity. Even though the water level is close to the analytical solution, the discharge is not conserved in the entire domain. Other 1D schemes as, for example, the Lateralized HLL, suffer from the same problem. The study presented in this work aims at a better understanding of this particular problem. It is divided in two parts. First, the model and the results are presented. Then, several changes are included in the model to highlight their impact on the solution. Finally, conclusions are drawn.